I am not a regular contributor to messages in this forum, but this one caught my eye.
On occasion, when setting a cane into a paperweight or a vase, either surface-decorated or cased, the cane can become distorted and various elements can disappear or become shaped differently from the intended design. I have a good example of this in a Scottish, Paul Ysart weight where, from the top, a clear cane design is seen, albeit a little fuzzy, but from the base, through the clear glass, that same cane looks quite different with several elements seen that are not in the top view. Unfortunately, my ISP seems to be having trouble displaying home pages right now, so I can't show you exactly what I mean.
I think the pink of the queried cane is identical to that of one of the flower canes and it may well be the same cane but the petals have warped over the central part which has then disappeared.
I have never heard of a signature cane in any Fratelli Toso or other similar maker's items. It would have been incredibly useful to collectors (and dealers) if they had used them, though.